Finite Group DatabasebetaFinite Group Databasebeta| order | 18666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C3 |
| direct product | C61×C3⋊D51 |
| unambiguous semidirect product | C3⋊(C61×D51) |
| unambiguous semidirect product | C17⋊(C3⋊D3×C61) |
| Fitting, socle, Hall | C32×C17×C61 ⋊ C2 |
| derived, Hall | C32×C17 ⋊ C2×C61 |
| Hall | C17×C61 ⋊ C3⋊D3 |
| Hall | C32×C61 ⋊ D17 |
| Sylow | C17 ⋊ C3⋊D3×C61 |
| Sylow | C32 ⋊ D17×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | C3⋊D51 |
| commutator, cosocle, hypocenter | C32×C17 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C61 | C2 |
| LCS | G ▷ C32×C17 | |
| UCS | C1 ◁ C61 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9333 |
4758 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C61×#10597479, #49152677, D3×C61×D51, … |
| maximal normal subgroup of | C61×#10597479, #49152677, D3×C61×D51, … |
| maximal quotient of | C61×C3⋊Dic51, C2×C61×C3⋊D51 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18666, 23);